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Math Help - i dont understand the notations.

  1. #1
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    i dont understand the notations.

    can someone help me with this question?
    let z = F(x, y) = x^2 -y +1

    b)find the functions g(x,y)= f( f(x,y) , y) and h(x,y)= f(x, (f(x,y) )
    c)If f(x,y)= f(y,x) and x cannot equal to y
    show that y= -x -1
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  2. #2
    Member ronaldo_07's Avatar
    Joined
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    Quote Originally Posted by KQ_jai View Post
    can someone help me with this question?
    let z = F(x, y) = x^2 -y +1

    b)find the functions g(x,y)= f( f(x,y) , y) and h(x,y)= f(x, (f(x,y) )
    c)If f(x,y)= f(y,x) and x cannot equal to y
    show that y= -x -1

    I think it means that for g(x,y) you put x^2 -y +1 in to x
    and for h(x,y) you put x^2 -y +1 into the y
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  3. #3
    Member arpitagarwal82's Avatar
    Joined
    Feb 2009
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    103
    a
    f( f(x,y) , y)
    = (x^2 -y +1)^2 -y +1


    b
    f(x,y)= f(y,x)
    => x^2 -y +1 = y^2 -x +1
    = >x^2 - y^2 = y - x
    => (x - y)(x + y) = y - x
    since x - y is not equal to zero, we can divide equation by x - y
    => x + y = -1
    => y= -x -1
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